A Software Defined Radio Implementation Using MATLAB Ziyi Feng Information Technology

Ziyi Feng
A Software Defined Radio Implementation
Using MATLAB
Information Technology
2013
FOREWARD
This project started in the January, 2013 and was completed in April, 2013. The
goal of this project is to design a radio communication system in audio band using
audio devices such as a sound card. The functions have been realized successfully.
I want to give my whole sincere and grateful appreciations to Principal Lecturer,
Dr. Chao Gao. As my supervisor of the thesis work, he tried his best to help me.
Without his help and guidance I cannot bring the theories into practice. Whenever
I met problems he came up with the solutions as soon as possible. Mr Gao is the
most patient teacher I have ever seen. I cannot thank him more.
On the other hand, I want to thank all my friends for their always supports
spiritual, fortunately we can share the last time in bachelor stage together.
1
VAASAN AMMATTIKORKEAKOULU
UNIVERSITY OF APPLIED SCIENCES
Degree program in Information Technology
ABSTRACT
Author
Ziyi Feng
Title
A Software Defined Radio Implementation Using MATLAB
Year
2013
Language
English
Pages
47
Name of Supervisor Chao Gao
Software Defined Radio (SDR) is a hot topic of wireless communication research
in recent years. The idea of SDR is to use ultra-high speed sampling and
ADC/DAC modules directly measure the received radio signal and decode
whatever it contains. The aim of this project is to study and understand SDR using
MATLAB in audio frequency band.
In this project, both analog and digital modulation and demodulation methods are
studied. Two Matlab sessions are set for sender and receiver respectively in
Windows 7. A simulation of signal modulation and demodulation can be
presented clearly just with Matlab.
2
TABLE OF CONTENTS
FOREWARD ....................................................................................................... 1
ABSTRACT ........................................................................................................ 2
LIST OF ABBREVIATIONS ............................................................................... 4
LIST OF FIGURES ............................................................................................. 5
LIST OF LISTINGS ............................................................................................ 7
1. INTRODUCTION ........................................................................................... 8
2. TECHNOLOGY BACKGROUND .................................................................. 9
2.1 Basic Concepts of Modulation and Demodulation ...................................... 9
2.2 Analog Modulation and Demodulation ....................................................... 9
2.2.1 AM Modulation and Demodulation .................................................. 10
2.2.2 FM Modulation and Demodulation .................................................. 12
2.3 Digital Modulation and Demodulation...................................................... 13
2.3.1 BPSK Modulation and Demodulation .............................................. 13
2.3.2 QPSK Modulation and Demodulation .............................................. 16
2.3.3 FSK Modulation and Demodulation................................................. 19
3. MATLAB IMPLEMENTATION .................................................................... 21
3.1 General Structure of System ..................................................................... 21
3.2 Modulator Implementation ....................................................................... 23
3.3 Demodulator Implementation ................................................................... 26
4. RESULTS AND ANALYSIS .......................................................................... 33
5. SUMMARY AND CONCLUSIONS .............................................................. 45
REFERENCES .................................................................................................. 46
3
LIST OF ABBREVIATIONS
AM
Amplitude Modulation
BFSK
Binary Frequency Phase-Shift Keying
BPSK
Binary Phase-Shift Keying
FM
Frequency Modulation
FWR
Full Wave Rectifier
LPF
Low Pass Filter
PM
Phase Modulation
QPSK
Quadrature Phase-Shift Keying
SDR
Software Defined Radio
4
LIST OF FIGURES
Figure 1Voltage define in AM .......................................................................... 10
Figure 2 Block diagram of coherent AM receiver ............................................. 11
Figure 3 Block diagram of non-coherent AM receiver ...................................... 12
Figure 4 Block diagram of BPSK transmitter ................................................... 14
Figure 5 Block diagram of BPSK receiver ....................................................... 14
Figure 6 Process of carrier recovery ................................................................. 15
Figure 7 Constellation map of QPSK ............................................................... 17
Figure 8 Block diagram of QPSK transmitter ................................................... 18
Figure 9 Block diagram of QPSK receiver ....................................................... 18
Figure 10 Block diagram of FSK transmitter.................................................... 19
Figure 11 Block diagram of FSK non-coherent receiver ................................... 20
Figure 12 Block diagram of radio communication system ................................ 21
Figure 13 Model of radio communication system............................................. 22
Figure 14 Block diagram of a normal communication system .......................... 22
Figure 15 Transmitter ...................................................................................... 33
Figure 16 Receiver .......................................................................................... 34
Figure 17 Original signal ................................................................................. 34
Figure 18 AM signal (modulated signal) .......................................................... 35
Figure 19 Received AM signal ......................................................................... 35
Figure 20 Received signal after FWR .............................................................. 35
Figure 21 Demodulated signal ......................................................................... 36
Figure 22 Carrier signal and modulated FM signal ........................................... 37
Figure 23 Received FM signal ......................................................................... 37
Figure 24 Demodulated signal ......................................................................... 38
Figure 25 Original signal ................................................................................. 38
Figure 26 Part of modulated BPSK signal ........................................................ 39
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Figure 27 Part of received BPSK signal ........................................................... 39
Figure 28 Truncated BPSK signal .................................................................... 39
Figure 29 Recovered carrier ............................................................................. 40
Figure 30 Demodulated signal ......................................................................... 40
Figure 31 Original signal ................................................................................. 41
Figure 32 Part of the received QPSK signal ..................................................... 41
Figure 33 Received QPSK signal ..................................................................... 41
Figure 34 Demodulated signal ......................................................................... 42
Figure 35 Original information ........................................................................ 42
Figure 36 Part of BFSK signal ......................................................................... 43
Figure 37 Received BFSK signal ..................................................................... 43
Figure 38 Signal after envelop detection .......................................................... 43
Figure 39 Demodulated signal ......................................................................... 44
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LIST OF LISTINGS
Listing 1 AM modulation ................................................................................. 23
Listing 2 FM modulation ................................................................................. 23
Listing 3 BPSK modulation ............................................................................. 24
Listing 4 QPSK modulation ............................................................................. 25
Listing 5 BFSK modulation ............................................................................. 26
Listing 6 AM demodulation ............................................................................. 27
Listing 7 FM demodulation.............................................................................. 27
Listing 8 BPSK demodulation ......................................................................... 29
Listing 9 QPSK demodulation ......................................................................... 31
Listing 10 BFSK demodulation........................................................................ 32
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1. INTRODUCTION
Traditional radio communication systems need a lot of hardware components such
as demodulator, detector, filter, etc. which makes the platform cost very high for
undergraduate level study and research. But the Laboratory exercises and studies
on that aspect are necessary for related teachers and students.
Software Defined Radio (SDR) makes it possible to implement the radio
communication process simply with software. Comparing to the traditional radio
communication systems, SDR omits all the hardware and replaces them by pure
software. This solution also gives a great advantage in flexibility because a SDR
receiver is able to decode all the signals.
However, the devices like A/D convertor, powerful signal processor still cost too
much for undergraduate level studies, some modifications have been done to
adjust the SDR to be suitable for students to use; it‟s what this project does. The
frequencies used in this communication system are limited into audio band, and so
it can be handled by a normal sound card. Thus the system can be constructed
with simple facilities. With this system students even can study radio
communication system at home only with a computer installed Matlab.
The project will employ one desktop PC with MATLAB installed and simulates
the radio communication process. Two Matlab sessions are executed at the same
time, one as transmitter, and the other as receiver. When the project works, the
signal is produced in transmitter and transmitted as sound after modulated. Then
the receiver will receive the signal by recording it. The information can be
obtained after demodulation. There are five modulation methods studied in this
project. The modulation and demodulation processes are designed according to
the related theory.
The rest of this thesis is arranged as follows. Chapter 2 describes the technology
background
which contains basic
ideas about
signal modulation and
demodulation ,also the five different methods are introduced; Chapter 3 explains
how the system implemented on Matlab; Chapter 4 presents the project results and
analysis; finally Chapter 5 concludes the work.
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2. TECHNOLOGY BACKGROUND
2.1 Basic Concepts of Modulation and Demodulation
In radio communication system the signal with high frequency has been
transmitted. On one hand, only the signal with high frequency can be transmitted
over a long distance; on the other hand, the height of antenna has a strong
relationship with the signal frequency. The lower the frequency is the higher the
antenna is. Thus to transmit low frequency signal may require a very high antenna
which even cannot be made out. Whenever the signal with low frequency needs to
be transmitted it is necessary and important to modulate it to a high frequency
signal. Only in this way can the signal be transmitted in the radio communication
system/1/.
The signal used to carry message is called carrier signal; typically it is a
high-frequency sinusoid or cosine waveform. The carrier signal can be transmitted
via the air over a long distance. The process of making the radio frequency carrier
signal carry the information signal with low frequency is modulation. Modulation
can be realized by varying one or more features of a carrier signal/2/.
When the receiver receives modulated signal, it has to process the modulated
carrier signal and get the original information; this process is demodulation. Its
function is opposite to that of modulation.
2.2 Analog Modulation and Demodulation
As said above modulation is the process of varying one or more features of a
carrier signal. If the modulating signal is analog and the variation for the
parameters of carrier signal based on the modulating signal is continuous, the
modulation is treated as analog modulation.
The parameters can be changed in carrier signal are amplitude and angle, while
the angle contains frequency 𝜔 and phaseθ. When the amplitude of carrier signal
varies as the modulating signal, it is amplitude modulation (AM); if the other two
parameters are changed, it is called frequency modulation (FM) and phase
modulation (PM) respectively/2/. AM and FM are focused in this project.
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2.2.1 AM Modulation and Demodulation
In amplitude modulation, the carrier signal‟s amplitude Vc varies in proportion to
the instantaneous amplitude of the modulating signal voltage 𝑒𝑚 /3/. Amplitude
modulation is a linear modulation process because of superposition principle/2/.
Figure 1 shows the defined voltage in amplitude modulation.
Figure 1Voltage define in AM
The modulation index is an important parameter that describes the degree of
modulation. It affects the shape of the AM signal and expressed as m=
𝑽𝒎
𝑽𝒄
(Vm, Vc
have been shown in the Figure 1). If the modulation index is more than 1, the
carrier signal will turn off when Vm equals the lowest amplitude. Thus m should
not be more than 1, namely m<=1, in other words Vm ≤ Vc .
Envelop of AM signal is an imaginary line drawn along the peak value of each
wave cycle. It can be expressed as 𝑒𝐸𝑁𝑉 =𝑉𝑐 + 𝑒𝑚 . As 𝑒𝑚 = 𝑉𝑚 ∗ 𝑠𝑖𝑛 𝜔𝑚 𝑡, the
envelop of AM becomes
𝑒𝐸𝑁𝑉 =𝑉𝑐 + 𝑉𝑚 ∗ 𝑠𝑖𝑛 𝜔𝑚 𝑡
(1)
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As m=
𝑉𝑚
𝑉𝑐
the Equation (1) can be changed to
𝑒𝐸𝑁𝑉 =𝑉𝑐 (1 + 𝑚 ∗ 𝑠𝑖𝑛 𝜔𝑚 𝑡)
(2)
The instantaneous voltage of AM signal 𝑒𝐴𝑀 should be the multiplication of the
envelop and the carrier signal, thus it can be expressed as 𝑒𝐴𝑀 = 𝑒𝐸𝑁𝑉 ∗ 𝑠𝑖𝑛 𝜔𝑐 𝑡,
namely,
𝑒𝐴𝑀 = 𝑉𝑐 (1 + 𝑚 ∗ 𝑠𝑖𝑛 𝜔𝑚 𝑡) ∗ 𝑠𝑖𝑛 𝜔𝑐 𝑡
(3)
eAM is the AM signal that has already get the information inside and used to be
transmitted to the receiver.
For the demodulation part, it is an opposite process of modulation. There are two
different methods to fulfill the demodulation, coherent and non-coherent. The
coherent demodulation can be used when the receiver knows the phase of the
received signal. The general coherent demodulation process is shown in Figure 2.
Figure 2 Block diagram of coherent AM receiver
As the Figure 2 shows, the received AM signal has to be multiplied by the carrier
signal produced by the local oscillator in receiver. The key procedure is that the
receiver must produce a carrier signal which has same phase and frequency with
the received signal‟s carrier signal.
The other method is non-coherent demodulation; it‟s used in this project. In
non-coherent method, the carrier signal is not necessary but the envelop line is
used. The demodulation process is shown in Figure 3.
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Figure 3 Block diagram of non-coherent AM receiver
Full wave rectifier converts the whole signal to DC. To be exactly it makes all the
inputs to be positive or negative. The low pass filter can be designed to let the
signals with expected frequency pass.
2.2.2 FM Modulation and Demodulation
Comparing to AM, FM has different properties. In FM modulation, the amplitude
of carrier remains constantly; while the frequency varies based on the modulating
signal. More specifically, the frequency deviation between carrier signal‟s original
frequency and its instantaneous frequency after modulating is in proportion to the
instantaneous amplitude of the modulating signal (input signal) /3/.
There is also a concept of modulation index in FM modulation, but it‟s completely
different from the AM‟s. In FM, the modulation index indicates how much the
modulated signal‟s frequency varies from the carrier signal‟s frequency. It is
defined as the ratio of maximum frequency deviation and the modulating signal‟s
frequency /4/ /5/. The formula is
𝑚=
∆𝑓
(4)
𝑓𝑚
Suppose the modulating signal is a cosine wave fm (t) and the carrier signal is
also a sine wave fc(t)=Acsin(2πfct), then the modulated signal should be
y(t)=Ac sin(2𝜋
𝑡
0
𝑓 𝜏 𝑑𝜏)
(5)
∆f
f(τ) is instantaneous frequency which should be (fc+ A *fm(t)), then we can
m
transfer the Equation (5) to be
y(t)=Ac sin(2𝜋
𝑡
(𝑓𝑐
0
=Ac sin (2𝜋fct+2𝜋
∆f
+ A ∗ 𝑓𝑚 𝜏 )𝑑𝜏)
m
(6)
∆f 𝑡
𝑓 (𝜏)𝑑𝜏)
Am 0 𝑚
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For fm(𝜏)=Amcos(2πfm𝜏),
𝑡
𝑓 (𝜏)𝑑𝜏=
0 𝑚
𝑠𝑖𝑛 ⁡(2𝜋 𝑓𝑚 𝑡)
Am
2𝜋 𝑓𝑚
y(t)= Acsin(2𝜋fct+2𝜋
∆f
Am
, then we can obtain
∗ 𝐴𝑚
𝑠𝑖𝑛 ⁡(2𝜋𝑓𝑚 𝑡)
2𝜋 𝑓𝑚
∆𝑓
= Acsin(2𝜋fct+𝑓 ∗ 𝑠𝑖𝑛⁡
(2𝜋𝑓𝑚 𝑡))
𝑚
In which
∆𝑓
𝑓𝑚
)
(7)
= m and y(t) is the modulated signal. Equation (7) shows the basic
theory of frequency modulation in mathematics.
For the demodulation part, similar with AM, FM also can be demodulated by
coherent and non-coherent methods. The coherent method is suitable for narrow
band FM signal and the receiver must know the phase shift of the received signal.
Thus the coherent method is only applied in a limit area. While the non-coherent
method has no this kind of limitation; it can be applied to both narrow band FM
and wide band FM.
In this project, the FM signal is demodulated by the function in Matlab. It‟s not so
accurate but useful.
2.3 Digital Modulation and Demodulation
The modulation process is digital modulation when the modulating signal is
digital. Compared with analog modulation, digital modulation has a lot of
advantages, for example greater noise immunity, greater security, etc. /6/. Similar
with analog modulation, there are three features can be modulated on carrier by
the digital information. Thus three major kinds of digital modulation technologies
are used in radio communication system. They are Amplitude-Shift Keying
(ASK), Frequency-Shift Keying (FSK) and Phase-Shift Keying (PSK). In this
project, one kind of FSK and two kinds of PSK are studied.
2.3.1 BPSK Modulation and Demodulation
BPSK stands for Binary Phase-Shift Keying which is the simplest PSK. In BPSK
the carrier signal‟s phase varies between two values according to the modulating
signal. BPSK is also called 2-PSK for the two values has 180°difference. The
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method to modulate carrier is when the signal is bit „1‟, the carrier‟s phase is one
value; while when the bit is „0‟, carrier‟s phase changes to another value. The pair
of phase 0 and π is used in this project.
Suppose carrier signal is y1=cos(2*pi*fc*t), phase of this carrier is 0,from
mathematic knowledge, it can be known that
y2= cos(2*pi*fc*t+pi)= -cos(2*pi*fc*t)= -y1
(8)
Equation (8) offers the method to modulate the signal. When signal is bit „1‟,
BPSK signal is y1, otherwise it‟s –y1. The process of modulation is shown in
Figure 4.
Figure 4 Block diagram of BPSK transmitter
For the demodulation part, there are both coherent and non-coherent methods. The
coherent one is used in the project. The process of demodulation is shown in
Figure 5.
Figure 5 Block diagram of BPSK receiver
In theoretical, received BPSK signal should be
r(t)=Acos(2 πfct+ kπ) (k=0,1)
(9)
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In this situation the carrier signal used to demodulate received signal can be as the
same as the transmitter‟s; process of carrier recovery can be omitted. But in reality,
received signal‟s phase is not only 0 or pi; it may have a phase shift φ. In this
situation, received BPSK signal is
r(t)=Acos(2 πfct+ kπ+𝜑) (k=0,1)
(10)
The demodulation result will be wrong if receiver still use the same carrier
recovery signal. To handle this problem carrier recovery circuit is used, which
means to get the carrier signal from the received signal itself. The process of
carrier recovery is described by Figure 6.
Figure 6 Process of carrier recovery
Carrier can be recovered from r(t) based on the following mathematic analysis
y=r2(t)=cos2(2 πfct+ kπ+ φ)
(k=0,1)
(11)
1
𝑦 = 𝐴2 (1 + cos⁡
(2 𝜋 ∗ 2𝑓𝑐 ∗ 𝑡 + 2𝑘𝜋 + 2𝜑)
2
1
=2 𝐴2 (1 + cos⁡
(2 𝜋 ∗ 2𝑓𝑐 ∗ 𝑡 + 2𝜑)
(12)
Let the signal y passes the high pass filter, the signal becomes
1
y’=2 𝐴2 cos⁡
(2 𝜋 ∗ 2𝑓𝑐 ∗ 𝑡 + 2𝜑)
(13)
At last, divide this signal‟s frequency to be half through a low pass filter, the
carrier signal can be recovered to
1
y’’=2 𝐴2 cos⁡
(2 𝜋 ∗ 𝑓𝑐 ∗ 𝑡 + 2𝜑)
(14)
Compare Equation (14) with Equation (10), we can find there is a phase
difference, this may lead to bad demodulation result. To get the right carrier signa,
y‟‟ has to be shift a phase of 𝜑. Finally the correct carrier is obtained
15
1
carrier=2 𝐴2 cos⁡
(2 𝜋 ∗ 𝑓𝑐 ∗ 𝑡 + 𝜑)
(15)
Receiver can multiply the received signal with this carrier signal to demodulate it.
The other method to overcome the phase shift problem is to use preamble.
Preamble means a certain sequence always transmitted before the real information.
With preamble, it can be known exactly when the signal starts. Receiver will
know the signal it should receive, in other words, receiver knows the phase it
should receive. Thus whenever signal has been received, receiver can cut the
signal from the expected phase. For example, if the preamble is 1 1, then the
signal‟s phase should be 0, when we receive signal like Equation (10), we can cut
it to be a signal expressed by Equation (9). This can be done by cutting the
received signal from one peak value (for cosine wave). To demodulate this signal,
just use the same carrier signal with transmitter is enough. In this situation, the
carrier signal can be produced by the receiver local oscillator.
Comparing these two methods, the second one is simpler. The first one is used in
this project to demodulate the BPSK signal but there is a little modification.
2.3.2 QPSK Modulation and Demodulation
Quadrature Phase-shift keying is another phase-shift modulation method which is
a little more complex than BPSK. It has twice the bandwidth efficiency of BPSK,
since two bits are transmitted in a single modulation symbol /6/.Two bits lead to
four different patterns „00‟,‟01‟,‟10‟ and „11‟. Thus the carrier signal‟s phase
varies among four values; each value stands for one pattern. The name Quadrature
comes from the feature of the four phases that the difference between two adjacent
pattern‟s phases is 90°.
There are two kinds of phase combinations which are usually used in modulation;
one is 0,π/2, π and 3π/2, the other one is π/4,3π/4,5π/4 and 7π/4.
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Figure 7 Constellation map of QPSK
The phase relationship can be seen clearly from Figure 7. The triangles show the
first phase combination, while the circles show the second phase combination.
The second phase combination is used in this project for the circuits and hardware
of producing these phases is easier to be realized in the real systems.
The information signal is transmitted bit by bit. As said before two bits form one
signal symbol, the bits stream should be separated to two sequences by breaking
two bits in one symbol before modulating carrier. Then for each sequence, the
modulation process is similar with BPSK (see Figure3). But the two carrier
signals for the two branches have two different phases. To make the modulated
signal QPSK has four phases of π/4,3π/4,5π/4 and 7π/4,one branch‟s carrier
signal should has the phase 0, while the other one has the phase π/2. The two
branches‟ outputs are added together to form the modulated QPSK signal. Figure
8 shows the process of QPSK modulation.
17
Figure 8 Block diagram of QPSK transmitter
For QPSK demodulation part, it also has coherent and non-coherent methods; we
use the coherent one. General process of QPSK coherent demodulation with
preamble is shown in Figure 9.
Figure 9 Block diagram of QPSK receiver
The „ctI‟ and „ctQ‟ in Figure 9 means the two different carrier signals mentioned
before. They are same with the carrier signals used in the corresponding
transmitter. In QPSK demodulation the problem of phase shift also exists and it
can be handled also by both carrier recovery and preamble; the basic theories have
been explained before. Preamble is used here and the sequence is „1111‟, so the
received signal should start at phase pi/4. When receiver receives QPSK signal it
truncates the signal from certain position. Then the truncated signal can be
demodulated with the carrier signals generated by local oscillator.
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2.3.3 FSK Modulation and Demodulation
Frequency-shift keying modulation is simpler than PSK. Binary FSK is the
simplest one in FSK modulation. In BFSK a pair of frequency is used to present
the signal bits „1‟ and „0‟. The carrier‟s frequency varies between two values
according to the signal state-binary 1 or 0/5/. The frequency for binary 1 is „mark‟
frequency while the other frequency for binary 0 is „space‟ frequency/7/.It also
can be seen as two carrier signals have same amplitude and phase but different
frequency and each carrier signal presents one signal state.
There are a lot of methods to make BFSK modulation, one of them is making use
of the feature that BFSK signal can be seen as formed by two carriers. For each
carrier, the amplitude of carrier varies according to the signal bits. Thus for each
branch it can be treated as Amplitude-shift keying (ASK). FSK signal can be seen
as sum of two ASK signals. ASK is easy to be produced by multiplying the
information signal with carrier signal directly. Figure 10 shows the process of
producing FSK signal with ASK theory.
Figure 10 Block diagram of FSK transmitter
Through Figure 10 we can see when signal bit is „1‟ carrier 1 will be kept and
carrier 2 will become to 0 after passing multiplier, then the FSK signal will be
carrier 1, otherwise FSK will be carrier 2. Thus FSK signal‟s frequency varies
based on signal bits.
For FSK demodulation part, the non-coherent method is used. Figure 11 shows
the process of non-coherent demodulation
19
Figure 11 Block diagram of FSK non-coherent receiver
BFSK signal can be demodulated easily with this process. From Figure 11 we can
see firstly let received signal pass two different band pass filters to get the
corresponding signal. And then through the envelop detector the two branches‟
information has been obtained. Lastly after making judgment and comparing two
branches‟ outputs the information is demodulated out.
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3. MATLAB IMPLEMENTATION
3.1 General Structure of System
A realistic SDR implementation should have some equipment, such as high speed
A/D convertor, powerful signal processor. That equipment makes the platform too
expensive for us students to study radio communication. To solve this problem
Matlab is used in this project and the radio signal‟s frequency is limited in audio
band.
When set up transmitter and receiver two Matlab sessions are used; one works as
transmitter and the other as receiver. All the modulation and demodulation works
are completed with Matlab programming. When use this system the user just
needs to choose the modulation and demodulation method and corresponding
parameters.
There are two ways to transmit the signal; one is over the air to simulate radio
communication, and the other is using a cable. The first one is major studied.
Figure 12 shows the basic structure of this radio communication system.
Figure 12 Block diagram of radio communication system
21
Figure 13 Model of radio communication system
Figure12 and Figure 13 show the radio communication system exactly. It can be
seen that just one laptop installed Matlab 2011Rb is enough to study the process
of radio communication.
Transmitting signal with cable has also been tested. It uses the same transmitter
and receiver, but the signal is transmitted by the cable.
Figure 14 Block diagram of a normal communication system
Figure14 shows the basic structure of a normal communication system simulated
by the Matlab. One extra sound card is needed to offer “line in” and “line out”
interfaces. One cable is also needed to transmit signal. This system works very
well but the soundcard may affect the signal a little. For example, it may cause a
22
lot of attenuation that leads to the result that a different modulated signal is
received by receiver.
3.2 Modulator Implementation
This modulator is designed to modulate five kinds of signal, AM, FM, BPSK,
QPSK and BFSK. Listing 1 will explain the detailsy about AM modulation.
%%%%This part is AM modulation; the first two lines define the carrier signal
and modulating signal. The carrier frequency fc and modulation index m can
be set dynamically. %%%%%%
carrier = 0.5*sin(2*pi*fc*t);
signal = sin(2*pi*fm*t);
am = (1+m*signal).*carrier;
% AM signal is generated based on the Equation
(3)
sound(am, FS); %This function is used to make the signal to be sound, the
signal is transmitted with this method.
Listing 1 AM modulation
For FM part, it‟s similar with AM, but the equation used to generate FM signal is
different.
%%%%This part is FM modulation; the modulating signal is put in the modulation
equation directly and frequency is fm. The carrier frequency fc and modulation
index mf can be set dynamically. %%%%%%
carrier = VC*sin(2*pi*fc*t);
% FM signal is generated based on the Equation (7).
FM = VC*sin(2*pi*fc*t+mf*sin(2*pi*fm*t));
sound(FM, FS);
%Transmit signal
Listing 2 FM modulation
Digital signal is a little more complex than analog signal. A sequence should be
generated firstly as the original modulating signal.
For BPSK, it is simply formed according to the block diagram shown in Figure 4.
23
%%%%This part is BPSK modulation; the carrier frequency fc can be set
dynamically. %%%%%%
carrier=0.2*cos(2*pi*fc*t);
%carrier signal
bk=[1 1 1 1 0 1 0 1 1 0 0 1];
bk2=[bk,bk];
% signal bits are preset
%% double the signal to transmit two times of signal once
bkt= kron (bk2,ones(1,fs));
% transfer the sequence into time domain
bktp= 2*bkt-1;
%modify the signal from unipolar to bipolar which means bit ‘0’ becomes to
‘-1’.
bpsk=bktp.* carrier;
% BPSK modulation based on Figure 4
sound(bpsk,fs);
Listing 3 BPSK modulation
In this modulation process, the original unipolar signal is changed to bipolar
signal. After multiply with carrier signal, when original bit is 1 the modulated
signal is same with carrier and the phase is 0; when original bit is 0 the modulated
signal will be –carrier. According to Equation (8) it is the original carrier signal
with 180 degree‟s phase shift in fact. Thus in modulated signal phase 0 presents
signal bit 1 and phase π presents signal bit 0.
For QPSK the basic modulation theory is similar but has some extra steps. This
modulator is designed according to Figure 8.
%%%%This part is QPSK modulation; the carrier frequency fc can be set
dynamically. %%%%%%
ctI = A0*cos(2*pi*fc*t);
ctQ = A0*cos(2*pi*fc*t + pi/2);
%% two carriers with two different phases
%1. Generate random binary stream bk and double it for the purpose of
transmitting twice signal once.
bk = [1 1 1 1 0 0 0 1 0 1 ];
bk=[bk,bk];
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%2. Separate bk into bkI and bkQ, then transfer them into time domain
respectively
bkI = bk(1:2:N);
bkQ = bk(2:2:N);
BKI = 2*(kron(bkI, ones(1,fs)))-1;
BKQ = 2*(kron(bkQ, ones(1,fs)))-1;
% 3. Multiply bkI with ctI, and bkQ with ctQ; modulate two branches according
to the similar theory with BPSK
branch1 = ctI.*BKI;
branch2 = ctQ.*BKQ;
% 4. Add the multiplication results together, it is QPSK
qpsk = branch1 + branch2;
%5.transmitte the original signal 2 times
sound(qpsk,fs);
Listing 4 QPSK modulation
At last, the BFSK signal can also be produced in this modulator. The process of
producing BFSK signal is totally different from PSK; it is designed based on
Figure 10.
%%%%This part is FSK modulation; the two carriers’ frequency f1 and f2 can
be set dynamically. %%
%%%There are two carrier signals with same amplitude and phase but different
frequency; each presents one signal state
carrier1=cos(2*pi*f1*t);
carrier2=cos(2*pi*f2*t);
1. Generate random binary stream bk and transfer them into time domain
bk=[1 1 1 1 0 1 0 1 1 1 0 0];
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bkt= kron (bk,ones(1,FS));
2. Generate two ASK signals. Signal bit 1 is presented by carrier 1’s frequency,
while signal bit 0 will be presented by the other carrier’s frequency.
ASK1=bkt.*carrier1;
ASK2= (-bkt+1).*carrier2;
3. Add two ASK signals together to get FSK signal
fsk =ASK1+ASK2;
Listing 5 BFSK modulation
3.3 Demodulator Implementation
Corresponding to transmitter, the receiver can also demodulate the five kinds of
modulated signals. Receiver is also designed that user can choose the
demodulation method and the corresponding parameters.
Firstly, it‟s AM signal. The AM signal is demodulated by the non-coherent
method. According to Figure 3 a full wave rectifier and a low pass filter should be
designed.
%% This part is AM demodulation part. It uses non-coherent method. %%%%%
recAM = audiorecorder (FS,16,1,1);
% construct a recorder object
recordblocking(recAM,T); % start to record the signal for T seconds
AM=getaudiodata(recAM);
%%get the signal data from the record object
%% The following command designs the full wave rectifier. When AM signal is
positive, (AM>=0) will return 1 and (AM<0) returns 0, then the positive signal
itself will be left. When AM signal is negative, (AM<0) will return 1, then
the signal (-AM) will be left. Signal’s negative part is converted to be
positive. In this way, the whole signal has been positive. The required full
wave rectifier’s function has been realized. %%
fwr = AM.*(AM>=0) + (-AM).*(AM<0);
%% This command designs a low pass filter. The first parameter defines the
order of the filter and the second parameter defines the frequency with which
the signal can pass the filter. %
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B = fir1(501, 0.001);
%%This is the last step; to filter the FWR output with the filter designed
before.%
demod = filter(B, 1, fwr);
Listing 6 AM demodulation
From Listing 6, we can see it is easy to handle the signal with the programming.
The signal is received by recording the sound, and then let the received signal
pass the full wave rectifier. At last after through the filter the original signal is
obtained.
For FM signal, the corresponding demodulation function in Matlab is used to
demodulate it.
%%This is the FM signal demodulation part; it uses the demodulation function
to demodulate it. %%%
% 1. Receive FM signal by recording and then get the recording data.
recFM = audiorecorder (FS,16,1,1);
recordblocking(recFM,T);
FM=getaudiodata(recFM);
% 2. Call the function ‘fmdemod()’ to demodulate the signal
signal= fmdemod(FM,fc,FS,mf*fm);
%3.design the required low pass filter. After the signal through the filter
the original signal can be demodulated out.
B = fir1(401, 2*fm/FS);
signal2 = filter (B,1,signal);
Listing 7 FM demodulation
Besides the above two analog demodulation methods, three digital demodulation
methods are also necessary. In digital part, both coherent and non-coherent
methods have been studied; more details are in the following part.
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Firstly, it‟s BPSK demodulation part. The coherent method is used to demodulate
the BPSK signal.
%% This is the demodulation part for BPSK signal; the carrier recovery has
been done in this part. %
recBPSK = audiorecorder (FS,16,1,1);
recordblocking(recBPSK,T);
BPSK=getaudiodata(recBPSK);
% 1. Truncate the signal from phase 0.
% find the average peak strength, then get the right peak value
BPSK2=FZY_smooth(BPSK);
[xr,locr]=findpeaks(BPSK2);
meanp = mean(xr);
[row,colmn]=find(xr>(meanp));
%cut the signal from the peak value, namely from the cosine wave’s 0 phase
BPSK2=BPSK2(locr(row(1)):end);
%2.recover the carrier from truncated signal BPSK2
B = fir1(822,1.83*fc/(FS/2),'high');
A=BPSK2.*BPSK2;
hpout=filter(B,1,A);
%high pass filter design
%make second power of the truncated signal
% let the power result pass high pass filter
% get the signal still from phase 0 to eliminate the high pass filter delay.
[x loc] = findpeaks(hpout);
ls=loc(50);
hpout2=hpout(ls:end);
%%divide the frequency to be the half; carrier signal’s frequency should be
fc, but the frequency of ‘hpout’ is 2fc.
fdout=interp(hpout2,2);
carrier=fdout(1:length(fdout)/2);
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%3. Demodulate the truncated BPSK signal with the recovered carrier
BL= fir1(4001,2.5e-4);
%low pass filter design
%multiply received signal with recovered carrier signal
y=BPSK2(1:length(carrier)).*carrier;
signal=filter(BL,1,y);
%pass the low pass filter
Listing 8 BPSK demodulation
BPSK signal is demodulated based on the process described in Figure5, but the
carrier recovery part is a little different from the description in Figure 6. Firstly,
the received signal BPSK has been truncated from phase 0 to be a new signal
BPSK2. The equation is
BPSK2 (t) =Acos(2 πfct+ kπ) (k=0)
However, for a signal r(t)=Acos(2πfct+ kπ) (k=0,1),no matter the value of k is 1 or
0 the carrier can be recovered from it according to the analysis in 2.3.1.and there
is no problem ofφ . Thus the carrier signal can be recovered from the BPSK2
without phase shift. The received signal can also be truncated from phase π ,and
carrier signal still can be recovered by the same process.
Then for QPSK signal, preamble is used to demodulate the received signal. The
sequence „1 1 1 1‟ is sent before other information signal bits. According to the
analysis in technology background part we can know that receiver should receive
the signal from phaseπ /4. Listing 9 is the demodulation part of QPSK signal.
%% This is the demodulation part for QPSK signal. Preamble is used to complete
that. The process of demodulation is described in Figure 9. %
recQPSK = audiorecorder (FS,16,1,1);
recordblocking(recQPSK,T);
QPSK=getaudiodata(recQPSK);
%1.cut the received signal from the expected phase.
% Find the received signal’s peak value and then make sure how many data should
be cut to get phase 0%%
29
QPSK2=FZY_smooth(QPSK);
[xr,locr]=findpeaks(QPSK2);
meanp = mean(xr);
[row,colmn]=find(xr>(meanp));
% the expected phase should be pi/4 for the bits 1 1 should be received. From
the expected phase to make sure how many data should be cut. %%%%
phasetime=pi/4/(2*pi)*(1/fc);
shift1=ceil(phasetime*FS);
ls1=locr(row(10));
% firstly cut the signal from the 0 phase to get signal QPSK2 and then cut
it to get truncated signal which starts from the expected phase.
QPSK2=QPSK2(ls1:end);
ls2=ls1+shift1;
QPSK3=QPSK2(shift1:end);%%%cut the signal from the pi/4 phase
%2.define the two carriers same with transmitter
ctI = cos(2*pi*fc*t3);
ctQ = cos(2*pi*fc*t3 + pi/2);
%3.demodulate the signal based on Figure 9
% multiply two carriers with the received signal respectively.
aip=QPSK3'.*ctI(1:length(QPSK3));
aqp=QPSK3'.*ctQ(1:length(QPSK3));
%design the low pass filter
BL=fir1(15000,5e-5);
% let the signal pass the low pass filter
aIPP=filter(BL,1,aip);
aQPP=filter(BL,1,aqp);
%4. Judge the signal, the accurate original signal can be obtained after
30
judgment.
aIPPP=aIPP>0;
aQPPP=aQPP>0;
Listing 9 QPSK demodulation
The demodulation of QPSK is realized by the codes in Listing 9. We can see the
process of carrier recovery can be omitted with the help of preamble. The results
are also very good. We will see that in Chapter 4.
Lastly, it comes to BFSK signal. The non-coherent method is used to demodulate
the received BFSK signal.
%% BFSK demodulation part%%%%%
recFSK = audiorecorder (FS,16,1,1);
recordblocking(recFSK,T);
FSK=getaudiodata(recFSK);
%1.through band pass filter%%%%%%%%%
%firstly, two different band pass filters are designed according to the
expected frequency values.BP1 is used to get signal represented by frequency
f1.BP2 is for frequency f2.%%%%
parang=[0.9,1.1];
Wn1=f1*parang/(FS/2);
BP1=fir1(101,Wn1,'bandpass');
Wn2=f2*parang/(FS/2);
BP2=fir1(101,Wn2,'bandpass');
%secondly, let received signal FSK passes the two band pass filters
respectively.
x1=filter(BP1,1,FSK);
x2=filter(BP2,1,FSK);
%2. Envelop detection %%%%%%%%%%%
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% Mathematically the envelope e(t) of a signal x(t) is defined as the magnitude
of the analytic signal (complex signal)/8/. Firstly modify the signal from
real to complex with the function of Hilbert ().
y1=hilbert(x1);
y2=hilbert(x2);
% based on the mathematic theory described before the absolute values of the
complex signal can be obtained with the function abs (). Envelop of received
signal is detected in this way.
envy1=abs(y1);
envy2=abs(y2);
%3.Sample&judge%%%%%%%%%%
% get the original signal from the two envelop signals
c1= (min (envy1) +max (envy1))/2;
c2= (min (envy2) +max (envy2))/2;
FSK1=envy1>c1;
FSK2=envy2>c2;
FSKOUT=FSK1>FSK2;
Listing 10 BFSK demodulation
The demodulation of BFSK signal has been done based on the process of
Figure 11. We can see the filters and other required functions can be completed
well with the software.
32
4. RESULTS AND ANALYSIS
Two windows will appear when the system works; one is transmitter, and the
other is receiver. They are designed by Matlab guide. Figure 15 and Figure 16
show the two GUIs. In the two GUIs, modulation methods and other
corresponding parameters can be set. These parameters must be same in both two
GUIs, or the result will be wrong.
Figure 15 Transmitter
Figure15 shows an example of choosing amplitude modulation. The carrier
frequency and modulation index should be chose from the available values. The
notice shows other information for this modulation. In receiver the method of
amplitude modulation and the same parameters should be set.
33
Figure 16 Receiver
The following part will show the modulation and demodulation results for all the
five modulation methods.
Firstly, it‟s AM signal. Figure 17, 18, 19, 20 and 21 show the situation of 1 kHz,
modulation index is 0.5.
Figure 17 Original signal
34
Figure 18 AM signal (modulated signal)
Figure 19 Received AM signal
Figure 20 Received signal after FWR
35
Figure 21 Demodulated signal
Figure 17 shows the signal needs to be transmitted. Figure 18 shows the
modulated signal. After transmitting via the air the received AM signal is shown
in Figure 19. The AM signal‟s shape still can be recognized, but it has a little
attenuation. The amplitude has been decreased a lot. This is because of the sound
card channel attenuation.
Figure 20 shows the signal after FWR. It can be seen clearly that the entire signal
has been positively, which verifies that the FWR works. At last Figure 21 shows
the demodulated signal. Comparing to Figure 17, we can see the original signal is
almost recovered from the received AM signal, but there is a litter attenuation and
delay. The attenuation is caused by both the channel (air) and the filter; however,
the delay is caused by the filter.
Secondly, it‟s FM signal. The frequency 1500 Hz and the modulation index 4 are
used to be an example.
In Figure 22, the first diagram shows the carrier signal. It can be figured out that
the signal‟s frequency is 1500 Hz. Then the second diagram shows the modulated
FM signal. It‟s obviously that the frequency varies as time and the variation is
regularly.
Figure 23 shows the received FM signal. The signal‟s frequency varies like the
FM signal in transmitter dose, but the amplitude changes. This is not correct in
normal situation, but it has no effect on demodulation process for the
demodulation only relies on the frequency variations.
36
Figure 22 Carrier signal and modulated FM signal
Figure 23 Received FM signal
37
However, it‟s still better to eliminate the amplitude variation in Figure 23, but it‟s
difficult in this system. Many methods have been tried to handle this problem, for
example adjust the value of frequency or the modulation index. Those methods
don‟t work. It has also been tried to lower the amplitude of the transmitted FM
signal for we guess maybe the sound card in laptop cannot handle that signal
strength. But it still fails. At last, we find that maybe it‟s because the attributes of
the laptop‟s speaker and microphone. There are other filters or amplifiers in those
two equipments which may change the signal a lot. If another better sound card is
installed in the laptop the results can be improved.
Figure 24 Demodulated signal
Figure 24 shows the demodulated signal; the frequency is the expected one. The
FM modulation and demodulation work well in this system.
Thirdly, the BPSK signal is tested. Carrier signal‟s frequency is 1500 Hz.
Figure 25 Original signal
38
Figure 26 Part of modulated BPSK signal
Figure 27 Part of received BPSK signal
Figure 28 Truncated BPSK signal
Figure 25 shows that the signal bit changes from 1 to 0 at fourth seconds. Then in
Figure 26 we can see the phase of the signal varies to pi to represent the bit 0. The
frequency of the signal is 1500 Hz as said before. Figure 27 shows the received
BPSK signal, although there are a lot of distortions it still can be seen that the
signal‟s phase has changed to pi suddenly like transmitted BPSK signal. The
variation causes amplitude fluctuations; however, it goes to nearly normal level
after a while.
39
As said in chapter three, the received BPSK signal is truncated to eliminate the
extra phaseφ . Figure 28 shows the truncating result in which the signal starts
from phase 0. For this received signal the carrier doesn‟t need to make a phase
change.
Figure 29 Recovered carrier
Figure 30 Demodulated signal
The carrier has been recovered successfully which is shown in Figure 29. The
value of the key parameter phase is 0 which is what we expect. The fact that the
recovered carrier signal‟s amplitude lower than the received BPSK signal‟s is
caused by the process of carrier recovery. The procedure of making power of
BPSK signal make the signal‟s amplitude decrease much.
Figure 30 shows the demodulate result. Comparing to Figure 25 the original
signal has been demodulated out successfully from received signal. However,
40
there are less signal bits than the original one because receiver starts later than
transmitter. Receiver hasn‟t received the first several bits.
Fourthly, it‟s QPSK signal. The carrier frequency is 1000 Hz in this example.
Figure 31 Original signal
Figure 32 Part of the received QPSK signal
Figure 33 Received QPSK signal
41
Similar with BPSK, the phase is also the key component in QPSK. In Figure 32 it
can be seen that the value of phase varies to 5pi/4 to represents binary bit “0 0”
which is what we expect in technology background part.
Figure 34 Demodulated signal
Figure 34 shows the demodulated result. It is almost same with the original
information shown in Figure 31. The preamble works very well but there are also
some delay which makes the demodulated signal has fewer signals than original
signal.
Lastly, it comes to BFSK signal; two carriers are needed to do that. The two
frequencies 3500Hz and 1000Hz are used to make the demonstration.
Figure 35 Original information
42
Figure 36 Part of BFSK signal
Figure 37 Received BFSK signal
Figure 38 Signal after envelop detection
43
Figure 39 Demodulated signal
Figure 36 shows that when signal bit changes from 1 to 0 the frequency of the
signal varies to a lower value. The frequency variation is obviously. Figure 37
shows the received BFSK signal. It has a big difference with transmitted BFSK
signal. The value of amplitude varies as the frequency; signal with lower
frequency has lower amplitude. Similar with FM modulation method this
phenomenon has little effect on demodulation but it shouldn‟t appear in normal
system. This also should be caused by the inner filters or amplifiers in laptop
speaker and microphone.
Figure39 shows that the BFSK demodulated result. The original signal bits have
been obtained except the first several bits.
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5. SUMMARY AND CONCLUSIONS
The system has been completed well. According to the results in fourth chapter
the system works well. In this system five modulation methods in totally have
been studied, two analog modulation methods and three digital ones. From this
project it can be known that phase modulation method is more difficult than
frequency modulation method for the receiver has to know the phase it should
receive. While in receiver the non-coherent demodulation method is usually used
for it doesn‟t care what the suitable carrier signal is. And the non-coherent
demodulation is also easier to be implemented with the circuits.
Through the construction process of this system, the modulation methods can be
studied more than the class in which only the theory part is known. What‟s more,
the equipment is simple and easy. To do this practice only one laptop installed
with Matlab is enough. Thus this system is suitable for students to study radio
communication by themselves. It is also can be a lab for students to enhance the
understanding of concept of modulation and demodulation. This system is
deserved to be studied.
Another benefit from this project is practicing the ability of signal processing.
When programming in Matlab, a lot signal processing method is needed, for
example to design a suitable filter. The filter designed in this system is not good
enough and can be improved.
For further study in this system, other modulation methods can be added in this
system and then they can be studied. Besides the modulation methods many other
aspects can be improved. For example to add preamble in transmitter signal and
then the receiver can be modified to check the preamble first. If the preamble is
right it keeps on receiving the signal or it can reject the transmitting. A checksum
also can be added in receiver to check if the signal is right.
45
REFERENCES
/1/ U.A.Bakshi, A.P.Godse 2009. Basic Electronics Engineering. Technical
Publications. Chapter 8.5.
/2/ Kundu Sudakshina 2010. Analog and Digital Communications. Pearson
Education India. pp. 163–184. ISBN 978-81-317-3187-1.
/3/ Warren Hioki 2001, Telecommunications 4/e, Prentice Hall,
/4/ About FM modulation. Accessed April 10,2013
http://en.wikipedia.org/wiki/Frequency_modulation
/5/ About FM modulation. Accessed April 10,2013
http://www.cdt21.com/resources/Modulation/modulation_FM.asp
/6/ Theodore
S.
Rappaport,
Theodore
Rappaport,
2002
Wireless
Communications: Principles and Practice (2nd Edition). Prentice Hall PTR, ISBN:
0130422320
/7/ FSK definition. Accessed April 16,2013
http://en.wikipedia.org/wiki/Frequency-shift_keying
/8/ Envelop detection. Accessed April 21,2013
http://www.mathworks.se/help/dsp/examples/envelope-detection.html
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